204 research outputs found
Creep via dynamical functional renormalization group
We study a D-dimensional interface driven in a disordered medium. We derive
finite temperature and velocity functional renormalization group (FRG)
equations, valid in a 4-D expansion. These equations allow in principle for a
complete study of the the velocity versus applied force characteristics. We
focus here on the creep regime at finite temperature and small velocity. We
show how our FRG approach gives the form of the v-f characteristics in this
regime, and in particular the creep exponent, obtained previously only through
phenomenological scaling arguments.Comment: 4 pages, 3 figures, RevTe
Avalanches in mean-field models and the Barkhausen noise in spin-glasses
We obtain a general formula for the distribution of sizes of "static
avalanches", or shocks, in generic mean-field glasses with
replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK)
spin-glass it yields the density rho(S) of the sizes of magnetization jumps S
along the equilibrium magnetization curve at zero temperature. Continuous
replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau
with exponent tau=1 for SK, related to the criticality (marginal stability) of
the spin-glass phase. All scales of the ultrametric phase space are implicated
in jump events. Similar results are obtained for the sizes S of static jumps of
pinned elastic systems, or of shocks in Burgers turbulence in large dimension.
In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple
interpretation relating droplets to shocks, and a scaling theory for the
equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are
discussed.Comment: 6 pages, 1 figur
Higher correlations, universal distributions and finite size scaling in the field theory of depinning
Recently we constructed a renormalizable field theory up to two loops for the
quasi-static depinning of elastic manifolds in a disordered environment. Here
we explore further properties of the theory. We show how higher correlation
functions of the displacement field can be computed. Drastic simplifications
occur, unveiling much simpler diagrammatic rules than anticipated. This is
applied to the universal scaled width-distribution. The expansion in
d=4-epsilon predicts that the scaled distribution coincides to the lowest
orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta),
zeta being the roughness exponent. The deviations from this Gaussian result are
small and involve higher correlation functions, which are computed here for
different boundary conditions. Other universal quantities are defined and
evaluated: We perform a general analysis of the stability of the fixed point.
We find that the correction-to-scaling exponent is omega=-epsilon and not
-epsilon/3 as used in the analysis of some simulations. A more detailed study
of the upper critical dimension is given, where the roughness of interfaces
grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146
Dynamics of particles and manifolds in a quenched random force field
We study the dynamics of a directed manifold of internal dimension D in a
d-dimensional random force field. We obtain an exact solution for and a Hartree approximation for finite d. They yield a Flory-like
roughness exponent and a non trivial anomalous diffusion exponent
continuously dependent on the ratio of divergence-free ()
to potential () disorder strength. For the particle (D=0) our results
agree with previous order RG calculations. The time-translational
invariant dynamics for smoothly crosses over to the previously
studied ultrametric aging solution in the potential case.Comment: 5 pages, Latex fil
2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions
We study elastic manifolds in a N-dimensional random potential using
functional RG. We extend to N>1 our previous construction of a field theory
renormalizable to two loops. For isotropic disorder with O(N) symmetry we
obtain the fixed point and roughness exponent to next order in epsilon=4-d,
where d is the internal dimension of the manifold. Extrapolation to the
directed polymer limit d=1 allows some handle on the strong coupling phase of
the equivalent N-dimensional KPZ growth equation, and eventually suggests an
upper critical dimension of about 2.5.Comment: 4 pages, 3 figure
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
Diffusion and Creep of a Particle in a Random Potential
We investigate the diffusive motion of an overdamped classical particle in a
1D random potential using the mean first-passage time formalism and demonstrate
the efficiency of this method in the investigation of the large-time dynamics
of the particle. We determine the -time diffusion {<{<
x^{2}(t)>}_{th}>}_{dis}=A\ln^{\beta} \left ({t}/{t_{r}}) and relate the
prefactor the relaxation time and the exponent to the
details of the (generally non-gaussian) long-range correlated potential.
Calculating the moments {}_{th}>}_{dis} of the first-passage time
distribution we reconstruct the large time distribution function itself
and draw attention to the phenomenon of intermittency. The results can be
easily interpreted in terms of the decay of metastable trapped states. In
addition, we present a simple derivation of the mean velocity of a particle
moving in a random potential in the presence of a constant external force.Comment: 6 page
Freezing of dynamical exponents in low dimensional random media
A particle in a random potential with logarithmic correlations in dimensions
is shown to undergo a dynamical transition at . In
exact results demonstrate that , the static glass transition
temperature, and that the dynamical exponent changes from at high temperature to in the glass phase. The same
formulae are argued to hold in . Dynamical freezing is also predicted in
the 2D random gauge XY model and related systems. In a mapping between
dynamics and statics is unveiled and freezing involves barriers as well as
valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe
Random Fixed Point of Three-Dimensional Random-Bond Ising Models
The fixed-point structure of three-dimensional bond-disordered Ising models
is investigated using the numerical domain-wall renormalization-group method.
It is found that, in the +/-J Ising model, there exists a non-trivial fixed
point along the phase boundary between the paramagnetic and ferromagnetic
phases. The fixed-point Hamiltonian of the +/-J model numerically coincides
with that of the unfrustrated random Ising models, strongly suggesting that
both belong to the same universality class. Another fixed point corresponding
to the multicritical point is also found in the +/-J model. Critical properties
associated with the fixed point are qualitatively consistent with theoretical
predictions.Comment: 4 pages, 5 figures, to be published in Journal of the Physical
Society of Japa
Glassy trapping of manifolds in nonpotential random flows
We study the dynamics of polymers and elastic manifolds in non potential
static random flows. We find that barriers are generated from combined effects
of elasticity, disorder and thermal fluctuations. This leads to glassy trapping
even in pure barrier-free divergenceless flows
(). The physics is described by a new RG fixed point at finite
temperature. We compute the anomalous roughness and dynamical
exponents for directed and isotropic manifolds.Comment: 5 pages, 3 figures, RevTe
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